Further Evidence on the Relation between Analysts’ Forecast Dispersion and Stock Returns

Further Evidence on the Relation between Analysts’ Forecast Dispersion and Stock Returns Orie E Barron Associate Professor Pennsylvania State University Smeal College of Business Administration University Park, PA 16802-1912 814-863-3230 Mary Stanford Associate Professor, Nobel Faculty Fellow Texas Christian University M.J Neeley School of Business Fort Worth, TX 76129 Yong Yu Pennsylvania State University Smeal College of Business Administration University Park, PA 16802-1912 September 29, 2005 (This is a preliminary revised draft of a manuscript requiring a major revision for publication Please not quote without permission) We gratefully acknowledge the contribution of I/B/E/S International Inc for providing earnings per share forecast data, available through the Institutional Brokers' Estimate System These data have been provided as part of a broad academic program to encourage earnings expectation research For their helpful comments we thank Richard Schnieble and workshop participants at the CUNY Baruch and Penn State University ABSTRACT Previous research finds a negative association between the level of dispersion in analysts’ earnings forecasts and subsequent stock returns This finding can be consistent with either unsystematic uncertainty that is priced positively because it increases a firm’s option value (Johnson, 2004) or overpricing due to a lack` of consensus among investors that limits the short sales of the most pessimistic traders (Diether et al, 2002) We use the Barron et al (1998) framework to measure the two theoretical variables that can both cause dispersion and cause it to be priced These are (1) uncertainty or (2) a lack of consensus (i.e., a relatively high level of private information among analysts) A high level of uncertainty may be priced positively or negatively depending on whether it is systematic or unsystematic In contrast, the private information that causes a lack of consensus is likely to be priced negatively because it reflects information asymmetry and a higher cost of capital (Botosan, Plumlee, and Xie 2004) The evidence we report helps distinguish between the different explanations for forecast dispersion and what drives its relation to stock returns We find that (1) changes in dispersion capture primarily changes in consensus (or changes in information asymmetry) whereas the level of dispersion captures primarily the level of unsystematic uncertainty (and not the level of information asymmetry), and (2) the uncertainty in forecast dispersion is negatively associated with future stock returns, but the lack of consensus (or information asymmetry) is positively associated with future stock returns These findings support Johnson’s option value explanation but not support Diether et al.’s overpricing explanation because lower levels of consensus not lead to lower future returns In addition, our evidence that levels and changes in dispersion reflect fundamentally different constructs reconciles the evidence on changes in dispersion presented by L’Her and Suret (1996) with the conclusions of Diether et al.(2002) and Johnson (2004), both of which are inconsistent with L’Her and Suret’s argument that forecast dispersion represents uncertainty that is priced negatively We find that increases in forecast dispersion coincide with more negative stock returns because there is less consensus (and thus more information asymmetry that adversely affects firms’ cost of capital) Introduction Prior research posits opposing explanations for the empirically documented relation between dispersion in analysts’ forecasts and stock returns Diether et al (2002) argue that the negative relation between dispersion levels and future returns is due to overpricing resulting from investor disagreement and limits on short sales that lead to optimistic current stock prices and lower future stock returns Johnson (2004) presents a model suggesting that this negative relation may also be due to the uncertainty (or risk) reflected in dispersion which, although unsystematic in nature, increases the option value of the firm and leads to lower future returns Further clouding the issue, Deither et al.’s arguments suggest a positive relation between changes in dispersion and contemporaneous stock returns This is contrary to evidence presented by L’Her and Suret (1996) that increases in forecast dispersion are negatively associated with stock returns Using the Barron, Kim, Lim, and Stevens (1998) (hereafter BKLS) decomposition of dispersion into uncertainty and lack of consensus we are able to distinguish between these opposing explanations Our evidence provides increased empirical support for Johnson’s conclusion that the level of dispersion analysts’ forecasts reflects unsystematic risk (uncertainty) In addition, consistent with L’Her and Suret’s (1996) findings, we find a negative relation between changes in dispersions and stock returns, which we show is likely caused by increased information asymmetry between informed and uninformed investors reflected in a decrease in consensus Diether et al (2002) argue that when investors disagree, limitations on trading, e.g., short sale limitations, result in prices that reflect the views of optimists but not pessimists This suggests a negative relation between dispersion levels and future stock returns when the overpricing is corrected and a positive relation between changes in dispersions and stock returns In addition, based on tests explaining dispersion with several measures of risk Diether et al conclude “…our results strongly reject the interpretation of dispersion in analysts’ forecasts as a measure of risk.” (p 2115) By contrast, Johnson (2004) provides a pricing model in which the negative relation between dispersion levels and stock returns may be due to a form of information risk (uncertainty) where dispersion reflects nonsystematic risk (idiosyncratic uncertainty) that increases the option value of the firm and lowers expected future returns However, as the author notes, his model is not inconsistent with Diether et al.’s overpricing argument, i.e., both may explain the relation between dispersion and returns We begin by empirically separating dispersion into its theoretical components Theoretically, in order for dispersion in analysts’ forecasts to exist there must be both (1) some uncertainty regarding future performance and (2) some lack of consensus due to the diversity of private information (Barry and Jennings 1992; Abarbanell, Lanen, and Verrecchia 1995; Barron, et al 1998) Thus, it is unclear the degree to which forecast dispersion reflects uncertainty or a lack of consensus Finding that dispersion levels reflect uncertainty rather than consensus would provide some support for Johnson’s (2004) hypothesis that dispersion levels reflect information risk Finding that changes in dispersion reflect changes in consensus would serve to increase understanding of the findings of L’Her and Suret (1996) and to reconcile these findings with those of Johnson (2004) and Diether et al (2002) We provide evidence on whether dispersion in analysts’ forecasts reflects uncertainty or a lack of consensus using the BKLS empirical proxies for these theoretical constructs We examine both the level of dispersion prior to an earnings announcement and the change in dispersion around earnings announcements.1 We find that the level of pre-announcement forecast dispersion reflects primarily uncertainty rather than a lack of consensus By contrast, changes in forecast dispersion reflect primarily changes in consensus rather than changes in uncertainty Our finding that levels of dispersion reflect uncertainty is consistent with Johnson’s (2004) conclusion that the negative relation between dispersion levels and future stock returns is driven by uncertainty In further analysis, we examine market data to determine whether the level of forecast dispersion reflects primarily systematic or unsystematic uncertainty about future performance We show that higher levels dispersion are associated with higher idiosyncratic risk and lower future returns This combined evidence provides support for Johnson’s argument that the negative relation between future returns and dispersion is due to investors’ unsystematic uncertainty and not overpricing Although this evidence lends support to Johnson’s theory it does not completely rule out Deither et al.’s (2002) conclusion that the negative relation results from overpricing due to investor disagreement However, Deither et al.’s argument that dispersion is negatively associated with future returns implies a positive (negative) relation between consensus (lack of consensus) and future stock returns because dispersion increases as consensus (lack of consensus) decreases (increases) In contrast Some prior studies measure the change in dispersion from year to year We not investigate these types of changes in forecast dispersion to the positive relation implied by the overpricing argument, we find a negative (positive) relation between consensus (lack of consensus) and future returns This finding also increases understanding of L’Her and Suret’s (1996) evidence that increases in dispersion coincide with decreases in stock returns Specifically, we show that increases in forecast dispersion coincide with decreases in consensus that reflect information asymmetry between informed and uninformed investors and that increases in dispersion coincides with decreases in stock returns Because low consensus stocks have high information asymmetry, this is also consistent with the positive relation between information asymmetry and the cost of equity capital hypothesized in Amihud and Mendelson (1986 and 1989), King et al (1990), Diamond and Verrecchia (1991), among others, and documented in previous studies (see Barron et al 2005 for further discussion) Uninformed investors demand a return premium to compensate for their risk of trading with privately informed investors This risk is not diversifiable since uninformed investors are always at a disadvantage relative to informed investors (O’Hara 2003) and demand to be compensated with higher expected future returns This evidence is of interest to accounting and finance researchers wishing to understand the relation between forecasts dispersion and stock returns For example, understanding that levels and changes in dispersion reflect different theoretical constructs can help researchers choose the appropriate proxy In addition, to the extent that dispersion is easily measured by investors while the BKLS measures are more complex and cannot be measured ex-ante our evidence allows investors as well as researchers to more precisely interpret the meaning of levels versus changes in forecast dispersion.2 Determining what forecast dispersion reflects the most is important to for methodological reasons For example, over fifty empirical studies published in selected top tier accounting and finance journals use analyst forecast dispersion as an empirical proxy for various firm characteristics Appendix lists papers published in The Accounting Review (15 papers), Journal of Accounting Research (11 papers), Journal of The discussion proceeds as follows Section describes our empirical proxies and research design as it relates to the strength of the associations between both levels of and changes in forecast dispersion, analysts’ uncertainty, and analysts’ lack of consensus (or diversity of information) Section investigates the relation between the two components of dispersion levels and future stock returns then provides evidence on the relation between dispersion levels and both systematic and unsystematic risk Section reconciles our evidence on changes in dispersion with prior research Section discusses robustness checks on the BKLS measures and alternate specifications Finally, section contains our conclusions Forecast Dispersion: Earnings Uncertainty or Lack of Consensus BKLS show how one can measure the theoretical constructs uncertainty and consensus by exploiting the fact that forecast dispersion and error in analysts’ forecasts reflect these theoretical constructs differently The intuition underlying their results stems from the fact that forecast dispersion and error differentially reflect error in analysts' common and idiosyncratic information The BKLS empirical proxies for consensus and uncertainty are: DISPERSION = V(1-) (1) CONSENSUS = ρ = 1-D/V (2) Where: D= dispersion in analysts’ forecasts, i.e., the sample variance of the individual forecasts (FCi ) around the mean forecast ( F C ), n measured as  ( FC i  F C ) (n  1) , where n is the number of i 1 Accounting and Economics (7 papers), Journal of Finance (4 papers) , Journal of Financial Economics (5 papers), Review of Accounting Studies (5 papers), Contemporary Accounting Research (7 papers), and Journal of Financial and Quantitative Analysis (3 papers) for the period 1990 to 2004 forecasts V= Uncertainty, i.e., the mean of the squared differences between individual analysts’ forecasts (FCi ) and reported earnings per n share (EPS) measured as  ( FCi  EPS ) n i 1 From equation (1), dispersion is the product of uncertainty (V) and lack of consensus (1ρ) Thus, forecast dispersion is simultaneously determined by both uncertainty and lack of consensus To understand the intuition for these measures it is helpful to consider the extreme examples where CONSENSUS is zero or one and a large number of forecasts (n) exist as described in Barron, Harris, and Stanford (2005) With a large number of forecast, the difference between the mean forecast ( F C ) and realized earnings per share (EPS) only reflects error due to common information because idiosyncratic error is averaged out of the mean When the mean forecast equals realized earnings CONSENSUS equals zero and D/V = When this is true, the BKLS model suggests that forecasts are based entirely on private information because all forecast error is idiosyncratic The difference between individual forecasts (FCi) and the mean forecast ( F C ) reflects error due to private information When all individual forecasts are exactly equal to the mean forecast CONSENSUS equals one and D/V = When this is true, the BKLS model suggests that forecasts are based entirely on common information because all forecast error is common Consistent with V reflecting overall uncertainty, if all forecasts exactly equal The relations we report between dispersion, consensus, and uncertainty are not merely mechaincal Theoretically, which component, V or (1-ρ), has more explainatory power for dispersion is, ex ante, not clear (Barron et al 1998) Also see Section for empirical evidence this relation is not merely mechanical realized earnings then V is equal to zero, consistent with perfectly accurate information, i.e., no uncertainty We investigate both the level of dispersion prior to earnings announcements and the change in dispersion estimated around earnings announcements and nonannouncement dates Specifically, we estimate the following models and use a Vuong test to compare the explanatory power of equation (3) and (4) to determine whether the level of dispersion in analysts’ forecasts is more highly associated with lack of consensus or uncertainty prior to the earnings announcement Similarly, comparing the explanatory power of equations (5) and (6) tests whether the change in dispersion around earnings announcements is better explained by changes in consensus or changes in uncertainty Log(D/P) = b0 +bLog(V/P) +   Log(D/P) = a0 +aLog(1-CONSENSUS)+   Δlog(D/P) d0 +d ΔLog(V/P) +   Δlog(D/P) c0 +c ΔLog(1-CONSENSUS) +   where Log(D/P) = natural log of dispersion D scaled by the stock price P D is preannouncement dispersion in analysts’ forecasts measured as the variance of analysts’ earnings forecasts issued within 30 days prior to the earnings announcement; Log(V/P) = natural log of overall uncertainty V scaled by the stock price P V is pre-announcement uncertainty estimated with equation (2) using forecasts issued within 30 days prior to the earnings announcement Log(1-CONSENSUS) = natural log of one minus pre-announcement consensus (i.e., lack of consensus) estimated with equation (1) using forecasts issued within 30 days prior to the earnings announcement Δlog(V/P) = change in natural log of overall uncertainty V scaled by the stock price P, estimated with equation (1) using forecasts issued within the 30-day preannouncement window and a 30-day post-announcement window Δlog(D/P) = change in the log-transformed dispersion D scaled by the stock price P, measured as the variance of the annual earnings forecast issued within the 30-day preannouncement window and a 30-day post-announcement window; Δlog(1-CONSENSUS) = change in the log-transformed lack of consensus (1 minus consensus), where consensus is estimated with equation (1) using forecasts issued within the 30-day pre-announcement window and a 30-day post-announcement window; Reported results scale dispersion (D) and uncertainty (V) by the stock price (P) measured at the end of the prior fiscal quarter We take the natural log of the variables for two reasons: first, BKLS demonstrates that dispersion is equal to the product of uncertainty and lack of consensus (i.e D=V(1- CONSENSUS)) Thus, it is natural to make this relation linear by taking the natural log; the second purpose is to mitigate skewness problems with dispersion and uncertainty 2.1 Sample Selection and Empirical Results The sample consists of quarterly and annual earnings per share forecasts from 1986 to 2003 Analysts’ earnings forecasts and actual earnings per share data are obtained from Institutional Brokers Estimate (I/B/E/S) Earnings announcement dates and other financial data are obtained from the quarterly COMPUSTAT Primary, Supplementary, or Tertiary file We investigate one-quarter-ahead forecast and two-year-ahead forecasts The one-quarter-ahead sample consists of quarterly forecasts measured within 30 days before the current quarterly earnings announcement The two-year-ahead sample consists of annual earnings forecasts measured within 30 days before the prior annual earnings announcement.6 To be included in the pre-announcement (levels) sample, two or more Our results and inferences are the same when we not scale by price and when we not log transform the variables IBES forecasts and actual data are adjusted historically for stock splits and rounded to two decimals in the summary file and four decimals in the detail file This rounding will introduce measurement errors into our main variables, e.g., artificially reducing forecast dispersion (see Payne and Thomas 2003 for a detailed discussion) To avoid this problem, we conduct our analyses on the raw forecast data, unadjusted for stock splits All results and inferences are the same for a one-year-ahead sample We 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